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Why are wires in simple circuits approximated as equipotentials? Because one of the three assumptions of circuit theory is: All electrical effects happen instantaneously throughout a circuit. If the circuit is small enough compared to the wave length of the signals applied, all electric signals travel through it so quickly, that we can assume that they ...

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I don't understand how to compute a finite resistance for an arc that would come out as infinite in some other cases. Arc formation is a sufficiently non-stationary and nonlinear process. So, one has to use dynamic circuit theory, where the resistivity in Ohm's law is a complex number and contains both active and reactive components depending on the ...

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The crucial fact about these idealized circuits and electric potential differences that leads to the assertion you want to justify is Wires are modeled as perfect conductors (Ohmic resistors with negligible resistance) for which there is zero potential difference between any two points. (This was edited from "perfect conductors are equipotentials.") If ...

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This is your circuit: The current that comes from the source, when reaches the point that must choose it's way, sees no difference between the two paths (symmetry) , so half of it flows through one way and the other part flows in the second way. It means that, $I_1=I_2$ , So the potential difference across yellow resistors is the same. It means that the ...

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First let's establish a feel for why they can be the same and then work out why they are indeed the same. The distances are not equal, but the resistance the test charge would face is also not the same, so the work might well be the same. This should show that the voltages can be the same. To find that they are indeed the same, we need not consider the ...

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What you are describing is called a series connection. Think of the batteries as pumps, with each pump generating 1.5 PSI. If you connect the outflow of one pump to the inflow of another, then overall the two pumps are going to generate 3.0 PSI. Note that the current capability is not doubled. If the two pumps are each rated for 1 gallon/minute, then the ...

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When electricity moves through anything -- wires or bodily tissues -- there are actual electrons (typically) moving. These electrons are being pulled along by an electric field, but they're also bumping into the atoms that make up the wire or bodily tissue. When an electron bumps into an atom, it transfers some of its kinetic energy to that atom. ...

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I mean, can I replace this configuration by one capacitor with one resistor in series such that this resistor is equivalent to the other two? The answer is actually no. For a single resistor and capacitor in series, the real part of the impedance is independent of frequency, i.e., the real part acts like a resistor. $Z_s = R_s + \frac{1}{j \omega ... 2 Yes, this would be a fair assessment of how the circuit is probably working. As a bit of an advisory, do not use the shower until you have traced the source of this!. It takes about 1mA for you to feel a tingling. Assuming it was dry when you were changing the light, then your resistance would be around 1-20kOhm in a damp environment (like a shower). This ... 2 Books say that ΣΔV=0 around a closed loop KVL holds only if the magnetic flux linking the circuit is unchanging. In ideal circuit theory, it is assumed that circuit elements are ideal lumped elements and the self inductance of the circuit is zero. In other words, we assume that the dimensions of the circuit and circuit elements are arbitrarily small ... 2 Ohm's law in the circuitry sense can be derived from the electromagnetic sense from the equation $$\vec J=\sigma\vec E$$ That is, current density is the conductivity times the electric field [with current density as the analog to current, conductivity the analog to the inverse of the resistance, and the electric field as the analog to voltage]. But this ... 2 For this particular circuit, the voltage across the R1/C1 branch #1 is fixed by V1, and that across R2 (branch #2) is also fixed, again by V1. That is, the fixed V1 decouples the two branches, so they can be solved separately (circuit #1 = voltage source V1 across branch #1, and circuit #2 = V1 across branch #2). Once these circuits are solved, the current ... 2 Some Examples of Non-Linear elements Diodes : Intensity$I = I_0 (e^{\frac{V}{V_T}}- 1) $, see examples of circuit with diodes Transistors: see for instance Transistors NPN, section "Large-signal models", to see Intensity/Voltage relations 2 I apparently cannot post images, so I apologize but you'll have to open this link in a new window to see my atrocious diagrams :) Diagrams -> http://i.imgur.com/Lxfu1e2.png EDIT: Here are the diagrams, sorry about my lack of artistic skills, haha. Voltage is an electrical potential difference, which is essentially a force caused by electrons wanting to ... 2 This is a simple consequence of Ohm's law, V=IR (note that this is by its very nature, an equation outside the realm of electro-statics, and that it is exact regardless of the drive frequency for a purely resistive element like a wire). A wire, by definition, has a very small resistance (precisely zero in the "ideal" case, some tiny number in most practical ... 1 This is a difference between theory and practice. I remember when I was beginning my studies I had lots of problems to understand why every teacher takes$\pi$as 3.14 and not 3.1415926..., as I learned in school. In algebra$\pi$was never calculated and the results were something like$2\sqrt2 \pi$. That was because in engineer calculations we don't care ... 1 Just to add to Alfred's detailed answer. The rule of thumb among the electron pushers is if the the physical structure exceeds 1/10 of a wavelength at the maximum frequency of its usage then it can not be considered a "lumped element" and Maxwell's EM equations need to be employed in the analysis. Up until that point the lumped element model works "for all ... 1 Without dependent sources, zeroing all the independent sources leaves a resistor network so that the Thevenin resistance can be calculated directly. However, dependent sources typically alter the Thevenin resistance so those can't be zeroed. One technique is to calculate the open circuit voltage and then place a wire across the nodes and calculate the ... 1 Symmetry is a powerful way to obtain a result by inspection. Here's how it works in this case. Remove the resistor between the A & B nodes. Now, it should be easy to see by inspection that the voltage between the A & B nodes must be zero for any$V_1$and$V_2$. The reason is symmetry. The left hand path is identical to the right hand path so it ... 1 I'm surprised the "real" schematic doesn't include a transformer turns ratio (actually, a model for the high voltage transformer, which has a primary winding with$N_p$turns connected to the power oscillatory circuit and a secondary winding with$N_s$turns (with$N_s > N_p$) connected to the discharge gap). Maybe everything is referenced to its ... 1 Without further information, it cannot be solved. That is, one cannot write$I = F(I_1,I_2)$a function of$I_1$and$I_2$alone. The best one could do it rewrite what you have above as$I = \frac{r_1}{r_1+r_2}I_1 + \frac{r_2}{r_1+r_2}I_2$which still requires knowledge of the internal resistance of the batteries. 1 but what is R in this formula? Since you're interested in what happens after the switch opens in both cases, redraw the circuit after the switch opens. In (1), there is just the one resistor R to the left of the switch so that's the resistance in the time constant. In (2), there is just the two series connected 1k resistors so R = 2k is the resistance ... 1 Power is the rate of transfer of energy i.e. it's the rate of doing work. When you write$Power = VI$you are assuming that there is some device consuming energy, and$V$is the voltage drop across this device. The device could be a resistor, that just turns the energy into heat, or it could be something like an electric motor that uses the energy to do work ... 1 Since you mention batteries in a comment: The voltage source + resistance model works well in many circumstances. At the extremes: high frequency / fast rise time waveforms: There will always be some inductance, from wiring if nothing else, which appears as an inductance, an easy add to the model. low frequency / long durations: As the battery ... 1 The basic idea is that all resistors can be modeled as a single material which has a resistance that is a function of either its cross-sectional area$A$or its length$L$only. This is because all resistors have$0<R<\infty$, and for any resistor,$R$is proportional to$L/A$. For example, for fixed$L$, there always exists such an$A$such that ... 1 Current is flow of charges - (1) Charges flow whenever there is an external$\vec E$i.e. an$\vec E$besides the charge's own field . So talking about electrostatic field$'\vec E'$which is present in DC circuits,considering ideal DC circuits,$\vec E\$ is present whenever there is a non zero potential difference between two points. Now you can use ...

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